Saturday, October 15, 2011

A Short Survey of Off-The-Shelf Solid Motors for Orbital Upper Stages

A Short Survey of Off-The-Shelf Solid Motors for Orbital Upper Stages

By Ed LeBouthillier

Many suggest using off-the-shelf solid motors (or similar custom motors) for upper stages of small orbital launchers. In this discussion, I review some of the requirements for upper stages and the possibility of using solids as upper stage motors. I will presume that a basic 1/4 pound (113 gram) payload is selected.

OFF THE SHELF MOTORS

High Power rocketry uses motors that provide many benefits for someone considering upper stages for orbital launchers. They are efficient, use modern propellants, come in a wide range of impulses and require little development.

The following table lists a few different solid motors that might be suitable for upper stages and their parameters:

First, the sea level Isp is derived from the published data (and verified as being reasonable). The equation is:

Avg Thrust * Burn Duration

Ideal Isp = --------------------------

Propellant Mass

These propellants are specified as being composite propellants. I used Propep as the

combustion code to estimate the Isp. I put Ammonium Perchlorate and HTPB into ProPep. I then set the mixture ratio similar to what is published as commonly used. I presumed that the published value represents 90% of the theoretical maximum Isp. Therefore, if 150 seconds is the value derived from published figures, then the theoretical ideal value of the Isp is 150 seconds / 0.90 = 166 seconds. I then adjusted the chamber pressure in Propep until I got a theoretical value equal to this Ideal Isp. I then calculated the Isp in a vacuum using Propep and then multiplied that value by 90% to get the vacuum Isp. It’s rough, but it gives meaningful statistics for comparison.

IMPLICATIONS

Based on the above figures, we can estimate the likely delta V from one of these motors.

If we presume no payload, and just the motor weight, then using the Aerotech I350R as an example we have:

dv = g * Isp * ln( Mf / Me )

dv = 9.8 * 235 * ln( 2294 g / 894 g )

dv = 2303 * ln( 2.57 )

dv = 2303 * 0.94

dv = 2164.82 m/s (7102 fps)

Since we need to provide about 7467.6 m/s (24500 fps) to 7772.4 m/s (25500 fps) in the upper stages, we would need about 7772 / 2165 = 4 stages at this performance level (for a total of 5 stages with a first stage). Presuming a 113 gram payload, a 113 gram guidance and control system for the 5th stage, we have:

Stage 5

Stage 4

Stage 3

Stage 2

Stage 1

Oxidizer

AP

AP

AP

AP

Lox

Fuel

HTPB

HTPB

HTPB

HTPB

Propane

Payload

0.113

2.5

39.5

619.5

9704.6

kg

OF Ratio

2.333

2.333

2.333

2.333

2.200

Oxidizer Density

1.949

1.949

1.949

1.949

1.141

g/cc

Fuel Density

0.919

0.919

0.919

0.919

0.582

g/cc

Avg Density

1.640

1.640

1.640

1.640

0.966

g/cc

Average Isp

235

235

235

235

252

seconds

Desired DeltaV

1867.4

1968.3

1968.3

1968.3

3172.7

m/s

Body:Fuel Mass (λ)

0.72

0.63

0.63

0.63

0.197

Payload Ratio

0.047

0.068

0.068

0.068

0.155

Structural Coef

0.419

0.387

0.387

0.387

0.165

Propellant Ratio

0.581

0.613

0.613

0.613

0.835

Mf/Me Ratio

2.249

2.349

2.349

2.349

3.610

Propellant Mass

1.402

22.711

356

5574

52152

kg

Oxidizer Mass

0.981

15.897

249

3901

35854

kg

Fuel Mass

0.421

6.814

107

1672

16297

kg

Oxidizer Volume

503.2

8154.5

127748.1

2001297.1

31423640.1

cc

Fuel Volume

457.3

7410.7

116096.3

1818760.5

28004727.9

cc

Stage Weight

2.411

37.018

580

9085

62425

kg

MT

1.009

14.308

224

3511

10274

kg

Me

1.123

16.832

264

4131

19978

kg

Mf

2.524

39.542

619

9705

72130

kg

Stage Impulse

3230

52338

819926

12844938

128880945

N-s

Cum delta V

1867

3836

5804

7772

10945

m/s

The important thing to notice is that the size of the 3rd stage is quickly too large (close to 620 kg [1370 lbs]). By the time you get to the second stage, it is up to 9705 kg (21000 lbs). The reason is that the performance is too low and weight too high for these motors. For a tiny 113 gram payload, the exo-atmospheric stages are 9705 kg.

SUMMARY

Based on this quick survey of a few commercial rocket motors (yes, it’s a small sample but I think it’s representative), we can see that typical off-the-shelf motors are likely too low in performance and too heavy for orbital launchers. This is not to say that these motors are not of high reliability and capability: they are highly engineered and quality products developed for the commercial market. They are safe and reliable and often reusable. However, these design choices work against them being the lightest possible and what is needed for orbital vehicles.